As I have previously mentioned in the blog you must be a T'Way Airlines member before you can buy or book a flight ticket. FYI, there are many budget airlines to Jeju Island; Jeju Air, Busan Air, Aseana Airlines, Korea Airlines. After going through the process, I found that the ticket can be as low as 15,000 won excluding the airport tax and fuel surcharge.
The ticket can be booked at least 2 weeks ahead. I bought one way ticket to Jeju Island with T'Way Airlines for 32,000 won and boarding was from Gimpo Airport. You may go to level 2F in Gimpo Airport to check in. Boarding time is 30 minutes before flight time and you can just check in with your passport and booking number.
After checked in, you will be given a boarding ticket printed by the officer. I was told that the maximum hand luggage is up to 10kg. Boarding is at level 1F and we have to ride a short journey bus(not even 5 minutes) to the plane. The flight to Jeju Island was packed and it took us about 1 hour 5 minutes to reach the island. We were served with free condiments and I opted for tomato juice for the first time in my life. Hmm... not bad as I imagine the taste could be.
The only bad experience I had was during the landing. The plane shook so bad as if the pilot didn't know how to brake!! :O I was scared shit! But still held it cool there..^__^ Alhamdulillah everything was alright.